198 MATHEMATICS
area of ✁ABC is given by
1
2
× base × height =
1
2
× 12 × 5 cm^2 , i.e., 30 cm^2
Note that we could also take 5 cm as the base and 12 cm as height.
Now suppose we want to find the area of an equilateral triangle PQR with side
10cm (see Fig. 12.2). To find its area we need its height. Can you find the height of
this triangle?
Let us recall how we find its height when we
know its sides. This is possible in an equilateral
triangle. Take the mid-point of QR as M and join it to
P. We know that PMQ is a right triangle. Therefore,
by using Pythagoras Theorem, we can find the length
PM as shown below:
PQ^2 =PM^2 + QM^2
i.e., (10)^2 =PM^2 + (5)^2 , since QM = MR.
Therefore, we have PM^2 = 75
i.e., PM = 75 cm = 53 cm.
Then area of ✁PQR =
1
2
× base × height =^2
1
10 5 3 cm 25 3
2